A laser or optical filament may be formed when a laser pulse with sufficiently high power undergoes self-focusing and consequently generates a plasma by ionizing the molecules of air (or by ionizing the molecules of a condensed state, through which it is propagating). A dynamic balance between diffraction, self-focusing and plasma defocusing ensures that the laser filament with its characteristically small beam size propagates over many Rayleigh lengths. For optical wavelengths in air at terrestrial densities, these filaments often require pulsewidths in the femtosecond to picosecond regime, whereas for shorter wavelengths, such as ultraviolet wavelengths, these filaments may be achieved with yet longer pulses, up to the nanosecond regime [see O. Chalus, A. Sukhinin, A. Aceves, J.-C. Diels, “Propagation of non-diffracting intense ultraviolet beams,” Optics Communications, Vol. 281, No. 12, pp. 3356-3360 (2008)]. Higher or lower air densities may change some of the self-focusing and propagation characteristics, but may support the same effects. Different gases and gas mixtures may also support the desired effects. A characteristic of a subset of these laser filaments, as well as the laser-plasma interaction w/solid materials and gases other than air, is their ability to generate a supercontinuum, or “white light”. This supercontinuum generation has been attributed to self-phase modulation, X-wave formation and four-wave mixing [see F. Theberge, M. Chateauneuf, V. Ross, P. Matthieu, J. Dubois, “Ultrabroadband conical emission generated from the ultraviolet up to the far-infrared during the optical filamentation in air,” Optics Letters, Vol. 33, No. 21, pp. 2515-2517 (2008)]. Spatial and temporal focusing techniques have been numerically explored for individual filaments in [see M. Kolesik, D. E. Roskey, J. V. Moloney, “Conditional femtosecond pulse collapse for white-light and plasma delivery to a controlled distance,” Optics Letters, Vol. 32, No. 18, pp. 2753-2755 (2007)], in order to explore control of the supercontinuum generation that accompanies a laser filament. Temporal focusing, by adjusting the chirp of a single broadband laser pulse, has been demonstrated in [see G. Mechain, C. D'Amico, Y.-B. Andre, S. Tzortzakis, M. Franco, B. Prade, A. Mysyrowicz, A. Couairon, E. Salmon, R. Sauerbrey, “Range of plasma filaments created in air by a multi-terawatt femtosecond laser,” Optics Communications, Vol. 247, pp. 171-180 (2005)] to achieve optimal ionization at long distances. Spectral reshaping of ultrashort pulses via filamentation in a gas cell or a waveguide at different pressures has also been investigated [see C. P. Hauri et al., “Generation of intense, carrier-envelope phase-locked few-cycle laser pulses through filamentation,” Applied Physics B, Vol. 79, pp. 673-677 (2004); and A. Couairon et al., “Pulse self-compression to the single-cycle limit by filamentation in a gas with a pressure gradient,” Optics Letters, Vol. 30, No. 19, pp. 2657-2659 (2005); and L. T. Vuong et al., “Spectral reshaping and pulse compression via sequential filamentation in gases,” Optics Express, Vol. 16, No. 1, pp. 390-401 (2008)] to reduce the pulse width and thereby increase the spectral content of the pulses. Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions was investigated [see K. Y. Kim et al., “Coherent control of terahertz supercontinuum generation in ultrafast laser-gas interactions”, Nature Photonics No. 2, pp. 605-609 (2008); and Z. Wang, “Generation of Terahertz via Nonlinear Optical Methods”, IEEE Transactions on Geoscience and Remote Sensing, vol. 1, no. 1 (2010)] in which terahertz generation in, semiconductors and nonlinear crystals, gases, super-broadband terahertz radiation (approx 75 THz), as well as an enhanced accompanying third harmonic generation were all explored. Using the methods disclosed here, all of these effects may be optimized through tailoring of the plurality of pulses generating them, including but not limited to the repetition rate, when the pulses are regularly space in time and may be characterized in terms of a repetition rate. X-rays have also been generated in the past, using laser pulses, in a variety of solid, liquid, gas and plasma/ionized media, including but not limited to in gases, rare gases, air, and water, as well as on solid targets and solid surfaces, including but not limited to semiconductors, metals and alloys, including metals and alloys containing elements of atomic number Z=11-45 and also including heavy metals and high-Z materials, including metals and alloys containing elements of atomic number Z>45.
In considering the concept of filament length, there are two aspects to consider. The first is the actual distance over which gas is ionized, representing the total ionized length, regardless of temporal dynamics, such that a time-integrated photograph would show this total ionized length. The second aspect is having a contiguous region, ionized simultaneously, such that an instantaneous photograph would capture the instantaneous ionized length. In the literature, there are several ways to extend the length of a laser filament.
These may include but are not limited to:
1. Increasing the laser energy and power—By increasing the energy of sub-100 fs pulses to over 100 mJ, propagation distances over 20 meters have been observed with multiple filaments. However, the break-up of the initial laser beam into multiple filaments occurs due to modulational instabilities. The formation of multiple filaments along the propagation direction of the laser pulse restricts the individual laser filament length to about 1 meter, although these filaments may be regenerated through dynamic spatial replenishment from the energy reservoir that surrounds them [see K. Stelmaszcyzk et al., “Long-distance remote laser-induced breakdown spectroscopy using filamentation in air,” Applied Physics Letters, Vol. 85, No. 18, pp. 3977-3979 (2004)].
2. Controlling the laser beam focusing—To avoid small-scale filamentation that is often associated with modulational instabilities, the initial laser beam may be weakly focused to generate a laser filament. This method provides a robust way to control the density, size and length of the plasma generated by the laser pulse. The use of an axicon lens has also been reported [see S. Akturk et al., “Generation of long plasma channels in air by focusing ultrashort laser pulses,” Optics Communications, Vol 282, pp. 129-134 (2008)] to generate long plasma channels. The temporal lifetime of this filament again depends on the plasma lifetime after the laser pulse interacts with the medium.
3. Concatenation of twin laser pulses—It has been shown [see S. Tzortzakis et al., “Concatenation of plasma filaments created in air by femtosecond laser infrared laser pulses,” Applied Physics B, Vol. 76, pp. 609-612 (2003)] that two sub-pulses with orthogonal polarization and separated by 100 fs may be concatenated to form a longer laser plasma in air. Given that the plasma lifetime is typically much longer than 100 fs, the temporal lifetime of this filament again depends on the plasma lifetime after the laser pulse interacts with the medium, which appears to be extended by the additional “orthogonal” excitation of the second pulse.
4. Using shorter wavelengths and longer pulse widths—When using shorter wavelengths, different mechanisms may be exploited by the laser pulse to ionize the air, increasingly incorporating multi-photon ionization as wavelength is decreased. In particular, ultraviolet pulses have been postulated to exploit this mechanism to result in much longer filaments, in that a single laser pulse may maintain a sufficient intensity to ionize gas without defocusing, thereby forming a longer filament in the sense of a longer spatial extent of time-integrated ionized gas, although temporally the actual length of a simultaneously contiguous plasma is still governed by the plasma lifetime, which is dictated by the ionization and recombination dynamics resulting from passage of each single pulse [see O. Chalus et al., “Propagation of non-diffracting intense ultraviolet beams,” Optics Communications, Vol. 281, No. 12, pp. 3356-3360 (2008)].
5. Extension of the plasma lifetime and/or revival of the plasma—To extend the lifetime of the electron plasma generated by a laser filament, a combination of femtosecond and nanosecond laser pulses has been adopted [see B. Zhou et al., “Revival of femtosecond laser plasma filaments in air by nanosecond laser,” Optics Express, Vol. 17, No. 14, pp. 11450-11456, (2009)]. In this technique, the short lived plasma channels generated in the wake of femtosecond laser pulses through filamentation in air may be revived after several milliseconds by a delayed nanosecond pulse, which is normally unable to ionize the air, without said air having first been ionized by the preceding more intense laser pulse.